Fig. 1: Schematic illustrating the concept of local-pseudogenerator protection.
From: Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators
The local pseudogenerator (LPG) \({\hat{W}}_{j}\) acts identically to the full generator \({\hat{G}}_{j}\) in the target gauge sector, but not necessarily outside of it. Starting in the target gauge sector \({{{{\bf{g}}}}}^{{{{\rm{tar}}}}}=({g}_{1}^{{{{\rm{tar}}}}},{g}_{2}^{{{{\rm{tar}}}}},\ldots ,{g}_{L}^{{{{\rm{tar}}}}})\), the ideal theory \({\hat{H}}_{0}\) propagates the dynamics within this sector, but experimentally unavoidable errors \(\lambda {\hat{H}}_{1}\) create transitions to other gauge-invariant sectors (gray). At sufficiently large but experimentally feasible values of the protection strength V, the LPG protection \(V{\hat{H}}_{W}=V{\sum }_{j}{c}_{j}({\hat{W}}_{j}-{g}_{j}^{{{{\rm{tar}}}}})\), with cj a suitably chosen sequence (see main text for details), will energetically penalize all gauge-noninvariant transitions. It will controllably suppress gauge violations in the thermodynamic limit for all accessible evolution times even when the error strength λ is not perturbative.
